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A012814 Take every 5th term of Padovan sequence A000931, beginning with the third term.

%I A012814 #54 Jul 27 2025 10:39:12
%S A012814 0,1,5,21,86,351,1432,5842,23833,97229,396655,1618192,6601569,
%T A012814 26931732,109870576,448227521,1828587033,7459895657,30433357674,
%U A012814 124155792775,506505428836,2066337330754,8429820731201,34390259761825,140298353215075,572360547759276,2334999585697905
%N A012814 Take every 5th term of Padovan sequence A000931, beginning with the third term.
%H A012814 Vincenzo Librandi, <a href="/A012814/b012814.txt">Table of n, a(n) for n = 0..1000</a>
%H A012814 Ulrich Brenner, Anna Hermann, and Jannik Silvanus, <a href="https://arxiv.org/abs/2012.05550">Constructing Depth-Optimum Circuits for Adders and AND-OR Paths</a>, arXiv:2012.05550 [cs.DM], 2020.
%H A012814 Sela Fried, <a href="https://arxiv.org/abs/2505.14196">Even-up words and their variants</a>, arXiv:2505.14196 [math.CO], 2025. See p. 7.
%H A012814 Taras Goy and Mark Shattuck, <a href="https://doi.org/10.61091/ojac19-01">Toeplitz-Hessenberg determinant formulas for the sequence F_n-1</a>, Online J. Anal. Comb. 19 (2024), no. 19, Paper #1, 27 pp. See Theorem 3.1.
%H A012814 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4,1).
%F A012814 a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).
%F A012814 a(n) = A000931(5*n+2).
%F A012814 G.f.: x/(1-5*x+4*x^2-x^3). - _Colin Barker_, Feb 03 2012
%F A012814 a(n) = A012855(n+4) - A012855(n+3).
%e A012814 G.f. = x + 5*x^2 + 21*x^3 + 86*x^4 + 351*x^5 + 1432*x^6 + 5842*x^7 + ...
%t A012814 LinearRecurrence[{5, -4, 1}, {0, 1, 5}, 25] (* _Vincenzo Librandi_, Feb 03 2012 *)
%o A012814 (Magma) I:=[0, 1, 5 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 03 2012
%Y A012814 Cf. A000931, A012855.
%K A012814 nonn,easy
%O A012814 0,3
%A A012814 _N. J. A. Sloane_
%E A012814 Initial term 0 added by _Colin Barker_, Feb 03 2012